Advertisements
Advertisements
Question
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Advertisements
Solution
We know that rationalization factor for `6 + 4sqrt2` is `6 - 4sqrt2`. We will multiply numerator and denominator of the given expression `(6 - 4sqrt2)/(6 + 4sqrt2)` by `6 - 4sqrt2` to get
`(6 - 4sqrt2)/(6 + 4sqrt2) xx (6 - 4sqrt2)/(6 - 4sqrt2) = (6^2 + (4sqrt2)^2 - 2 xx 6 4 sqrt2)/((6)^2 - (4sqrt2)^2)`
` (36 + 16 xx 2 - 48sqrt2)/(36 - 16 xx 2)`
`= (36 + 32 - 48sqrt2)/(36 - 32)`
`= (68 - 48sqrt2)/4`
`= 17 - 12sqrt2`
Hence the given expression is simplified with rational denominator to `17 - 12sqrt2`
APPEARS IN
RELATED QUESTIONS
Simplify the following expressions:
`(11 + sqrt11)(11 - sqrt11)`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Classify the following number as rational or irrational:
`(3+sqrt23)-sqrt23`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
